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A190644
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Least number k>1 such that (tau(k-1)+tau(k+1))/tau(k) = n where tau = A000005.
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1
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6, 34, 39, 7, 11, 19, 29, 41, 79, 71, 179, 199, 181, 239, 883, 419, 701, 839, 881, 1429, 2351, 1259, 1871, 2161, 4049, 3079, 3361, 2521, 6481, 4159, 6299, 5279, 11551, 5039, 20789, 7561, 25919, 10079, 16561, 13441, 38611, 13859, 23761, 21839, 100673, 20161
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OFFSET
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1,1
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LINKS
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MAPLE
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with(numtheory):
a:= proc(n) local k;
for k from 2 while (tau(k-1)+tau(k+1)) /tau(k)<>n do od; k
end:
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MATHEMATICA
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tau = DivisorSigma[0, #]&;
a[n_] := For[k=2, True, k++, If[(tau[k-1]+tau[k+1])/tau[k]==n, Return[k]]];
Module[{nn=300000, tau}, tau=(#[[1]]+#[[3]])/#[[2]]&/@Partition[DivisorSigma[ 0, Range[nn]], 3, 1]; Flatten[Table[Position[tau, n, 1, 1], {n, 50}]]+1] (* Harvey P. Dale, Nov 24 2022 *)
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PROG
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(Sage)
tau = number_of_divisors
return next((k for k in IntegerRange(2, infinity) if tau(k-1)+tau(k+1) == n*tau(k))) # D. S. McNeil, May 19 2011
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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